The need for a review is pressing. Screening always sounds good – catch disease early, while it can still be treated – but the reality is more complex and screening has side effects. The problem is that doctors and researchers have known about these downsides of screening for decades, but the message hasn't got through to patients.

It is this failure of communication that has led several prominent UK doctors to say publicly that they have chosen not to have breast cancer screening, including Fiona Godlee, the editor of the BMJ, Iona Heath, a London GP and former president of the Royal College of GPs, and Susan Bewley, professor of complex obstetrics at King's College London. As Heath writes in the BMJ, "My worry is that I have made my decision on the basis of information that is not readily available to my patients."

So what is this crucial information? Overdiagnosis – picking up "diseases" that were never going to cause any problem – is a major problem in most screening programmes.

In the case of breast cancer screening, the mammograms will find lesions of uncertain significance – cancers that do not behave aggressively. Because we do not usually have the ability to work out which of these cancers will spread and cause death, all women are offered treatment, which can include mastectomy and radiation therapy. These treatments can do harm. For example, radiotherapy slightly raises the risk of later heart disease and surgery comes with the usual risks from the anaesthetic and the potential for infection. These risks may well be worth taking if the breast disease threatens your life, but it is far less clear what to do when the screening has picked up a potentially harmless lesion.

Another problem with assessing the benefits of screening is "lead time bias". Take two men with prostate cancer that began in 2011. One is picked up in 2011 through PSA (prostate-specific antigen) screening, and the other is picked up in 2013, because symptoms have developed. They both die in 2015. It will look as though the man detected by screening lived for longer after his diagnosis compared with the man who was picked up through symptoms. The screening didn't actually extend life, but if we just count the years of survival after diagnosis it will look as though screening did lead to a longer life. Analysis of screening frequently falls into this trap, making it look far better than it is.

Then there is the effectiveness of the screening intervention. GPs have recently been contracted to screen at-risk people for dementia. But the tests used are highly inaccurate. For example, if six out of 100 people have dementia, then testing will pick up 4 of them – but will also identify 23 people as having dementia who in reality do not. Generating so many false positives and negatives creates much misery and anxiety. Yet because the screening tests are offered "opportunistically", when GPs are seeing patients who have come about something else, people may be taken unaware and not get a chance to consider whether or not they want to risk the potential harms caused by such a bad test.

All this means that patients may not know if their screening test has caused them harm. This leads to the "popularity paradox" where a bad screening test creates many false positives, and much unnecessary treatment, but people end up feeling that they "owe their life" to screening when, in reality, they have been subjected to unnecessary treatments – and the resultant risks.

Even doctors find the benefits of screening hard to analyse correctly. Psychologist Gerd Gigerenzer has investigated this, using figures for a screening test for bowel cancer as an example. If the prevalence of cancer is 0.3%, the sensitivity of the test was 50% and the false positive rate was 3%, the doctors were asked, what is the probability that someone who tests positive actually has colorectal cancer?

Half the doctors gave the answer as 50%, when the result is actually less than 5%. Imagine you have a representative sample of 10,000 people: 0.3%, or 30, of them will have bowel cancer. The test is 50% sensitive, picking up 15 of them. However, the false positive rate is 3%, which will be 3% of the 9,970 who don't have bowel cancer, or 299 people. So there are 299 + 15 positive tests, but only 15 out of 314 are true positives. In other words, when a test result comes back positive, the probability that the patient has bowel cancer is only 5%. Screening tests can often perform less well than the numbers might look.

The NHS has made some efforts to improve the information that patients get when they are invited for screening, but it still does not make explicit the risks of treatment for "cancers" that would never otherwise have done harm.

The media launch of the new leaflet for breast cancer screening last year was marred by a spokesperson from the Breast Cancer Campaign telling women they should be aware of the hazards of screening but should "attend screening appointments when invited". This is nonsensical – adults should be able to decide for themselves which risks they would prefer to accept.

It is precisely because screening is a mixed bag of benefit and harm that no one should impose their own values onto another person. Yet at present, NHS screening programmes are judged by how many people attend, and not by how many people make an informed choice to attend – or not. Similarly, GPs are paid according to how many screenings are done, not by how well informed their patients are.

In addition, patients are often misled into thinking that invitations to NHS screening come from their trusted GP rather than where they actually come from – a central NHS Screening office. Apparently this increases uptake.

We need a debate about the cost-effectiveness of our screening sacred cows, but we also need a debate about how to give autonomous adults fair information about screening that respects their right to decline. Until patients are given unbiased information – including that screening can maim as well as help – we will continue to fall short of the ideal of patient consent, "no decision about me – without me".

• This article was corrected on 6 January 2014. The original picture caption used the term "false positives" when in fact the problem is the discovery of real tumours that may or may not be dangerous. This has been amended.